Pearson correlation of offspring and parental data

The Pearson correlation coefficient seems like a useful measure of how strongly the beak depth of parents are inherited by their offspring. Compute the Pearson correlation coefficient between parental and offspring beak depths for G. scandens. Do the same for G. fortis. Then, use the function you wrote in the last exercise to compute a 95% confidence interval using pairs bootstrap.

Remember, the data are stored in bd_parent_scandens, bd_offspring_scandens, bd_parent_fortis, and bd_offspring_fortis.

This exercise is part of the course

Statistical Thinking in Python (Part 2)

Exercise instructions

Use the pearson_r() function you wrote in the prequel to this course to compute the Pearson correlation coefficient for G. scandens and G. fortis.
Acquire 1000 pairs bootstrap replicates of the Pearson correlation coefficient using the draw_bs_pairs() function you wrote in the previous exercise for G. scandens and G. fortis.
Compute the 95% confidence interval for both using your bootstrap replicates.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Compute the Pearson correlation coefficients
r_scandens = ____
r_fortis = ____

# Acquire 1000 bootstrap replicates of Pearson r
bs_replicates_scandens = ____

bs_replicates_fortis = ____


# Compute 95% confidence intervals
conf_int_scandens = ____
conf_int_fortis = ____

# Print results
print('G. scandens:', r_scandens, conf_int_scandens)
print('G. fortis:', r_fortis, conf_int_fortis)

Edit and Run Code

This exercise is part of the course

Statistical Thinking in Python (Part 2)

IntermediateSkill Level

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When doing statistical inference, we speak the language of probability. A probability distribution that describes your data has parameters. So, a major goal of statistical inference is to estimate the values of these parameters, which allows us to concisely and unambiguously describe our data and draw conclusions from it. In this chapter, you will learn how to find the optimal parameters, those that best describe your data.

Exercise 1: Optimal parameters Exercise 2: How often do we get no-hitters?Exercise 3: Do the data follow our story?Exercise 4: How is this parameter optimal?Exercise 5: Linear regression by least squares Exercise 6: EDA of literacy/fertility data Exercise 7: Linear regression Exercise 8: How is it optimal?Exercise 9: The importance of EDA: Anscombe's quartet Exercise 10: The importance of EDA Exercise 11: Linear regression on appropriate Anscombe data Exercise 12: Linear regression on all Anscombe data

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Exercise 1: Generating bootstrap replicates Exercise 2: Getting the terminology down Exercise 3: Bootstrapping by hand Exercise 4: Visualizing bootstrap samples Exercise 5: Bootstrap confidence intervals Exercise 6: Generating many bootstrap replicates Exercise 7: Bootstrap replicates of the mean and the SEM Exercise 8: Confidence intervals of rainfall data Exercise 9: Bootstrap replicates of other statistics Exercise 10: Confidence interval on the rate of no-hitters Exercise 11: Pairs bootstrap Exercise 12: A function to do pairs bootstrap Exercise 13: Pairs bootstrap of literacy/fertility data Exercise 14: Plotting bootstrap regressions

You now know how to define and estimate parameters given a model. But the question remains: how reasonable is it to observe your data if a model is true? This question is addressed by hypothesis tests. They are the icing on the inference cake. After completing this chapter, you will be able to carefully construct and test hypotheses using hacker statistics.

Exercise 1: Formulating and simulating a hypothesis Exercise 2: Generating a permutation sample Exercise 3: Visualizing permutation sampling Exercise 4: Test statistics and p-values Exercise 5: Test statistics Exercise 6: What is a p-value?Exercise 7: Generating permutation replicates Exercise 8: Look before you leap: EDA before hypothesis testing Exercise 9: Permutation test on frog data Exercise 10: Bootstrap hypothesis tests Exercise 11: A one-sample bootstrap hypothesis test Exercise 12: A two-sample bootstrap hypothesis test for difference of means

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Exercise 1: A/B testing Exercise 2: The vote for the Civil Rights Act in 1964 Exercise 3: What is equivalent?Exercise 4: A time-on-website analog Exercise 5: What should you have done first?Exercise 6: Test of correlation Exercise 7: Simulating a null hypothesis concerning correlation Exercise 8: Hypothesis test on Pearson correlation Exercise 9: Do neonicotinoid insecticides have unintended consequences?Exercise 10: Bootstrap hypothesis test on bee sperm counts

Every year for the past 40-plus years, Peter and Rosemary Grant have gone to the Galápagos island of Daphne Major and collected data on Darwin's finches. Using your skills in statistical inference, you will spend this chapter with their data, and witness first hand, through data, evolution in action. It's an exhilarating way to end the course!

Exercise 1: Finch beaks and the need for statistics Exercise 2: EDA of beak depths of Darwin's finches Exercise 3: ECDFs of beak depths Exercise 4: Parameter estimates of beak depths Exercise 5: Hypothesis test: Are beaks deeper in 2012?Exercise 6: Variation in beak shapes Exercise 7: EDA of beak length and depth Exercise 8: Linear regressions Exercise 9: Displaying the linear regression results Exercise 10: Beak length to depth ratio Exercise 11: How different is the ratio?Exercise 12: Calculation of heritability Exercise 13: EDA of heritability Exercise 14: Correlation of offspring and parental data Exercise 15: Pearson correlation of offspring and parental data

Current Exercise

Exercise 16: Measuring heritability Exercise 17: Is beak depth heritable at all in G. scandens?Exercise 18: Final thoughts